REMAINING LAWS OF NATURE. 161 



The laws of equality and inequality between spaces, 

 or between numbers, have no connexion with laws of 

 causation. That the angle of reflexion is equal to the 

 angle of incidence is a statement of the mode of action 

 of a particular cause ; but that when two straight lines 

 intersect each other the opposite angles are equal, is 

 true of all such lines and angles, by whatever cause 

 produced. That the squares of the periodic times of 

 the planets are proportional to the cubes of their dis- 

 tances from the sun, is an uniformity derived from 

 the laws of the causes which produce the planetary 

 motions, namely, the central and the tangential force; 

 but that the square of any number is four times the 

 square of half the number, is true independently of 

 any cause. The only laws of resemblance, therefore, 

 which we are called upon to consider independently 

 of causation, belong to the province of mathematics. 



4. The same thing is evident with respect to the 

 only remaining one of our five categories, Order in 

 Place. The order in place, of the effects of a cause, 

 is (like everything else belonging to the effects) a 

 consequence of the laws of that cause. The order in 

 place, or, as we have termed it, the collocation, of the 

 primeval causes is (as well as their resemblance) in 

 each instance an ultimate fact, in which no laws or 

 uniformities are traceable. The only remaining gene- 

 ral propositions respecting order in place, and the 

 only ones which have nothing to do with causation, 

 are some of the truths of geometry; laws through 

 which we are able, from the order in place of certain 

 points, lines, or spaces, to infer the order in place of 

 others which are connected with the former in some 

 known mode; quite independently of the particular 

 nature of those points, lines, or spaces, in any other 



VOL. II. M 



